Maxima integral wrong #18599
Description
See
- https://groups.google.com/forum/#!topic/sage-devel/GX-hYs0grdE
- https://groups.google.com/forum/#!topic/sage-devel/PSWsQPl1TBA
sage: from sage.symbolic.integration.external import maxima_integrator
sage: maxima_integrator(sqrt(cot(x)^2),x)
-1/2*log(tan(x)^2 + 1) + log(tan(x))
sage: maxima_integrator(cot(x),x)
log(sin(x))
sage: maxima_integrator(sqrt(cot(x)^2),x,pi/4,3*pi/4)
0
sage: maxima_integrator(cot(x),x, pi/4,3*pi/4)
0
sage: f(x) = maxima_integrator(sqrt(cot(x)^2),x)
sage: f(pi/4)
-1/2*log(2)
sage: f(3*pi/4)
I*pi - 1/2*log(2)
But that is wrong, as this function is nonnegative and usually positive. The problem is in Maxima.
(%i1) domain:complex;
(%o1) complex
(%i2) sqrt(cot(x)^2);
2
(%o2) sqrt(cot (x))
(%i3) integrate(sqrt(cot(x)^2),x,%pi/4,%pi/4*3);
(%o3) 0
(%i4) integrate(sqrt(cot(x)^2),x);
2
log(tan (x) + 1)
(%o4) log(tan(x)) - ----------------
2
Reported upstream at bug 2971.
Upstream: Reported upstream. No feedback yet.
Component: calculus
Issue created by migration from https://trac.sagemath.org/ticket/18599